On Tue, 7 Dec 2004, Timothy Y. Chow wrote:
> Petrus H. Potgieter has posted an interesting paper on hypercomputation
> to the Los Alamos ArXiv.
>>http://arxiv.org/abs/cs/0412022
Last night I downloaded the paper and I read it. On page 5, the author
describes how an accelerating Turing machine (ATM) can solve the halting
problem. But he notes that there exists no ATM that can solve the halting
problem for ATMs. However, he does not describe the halting problem for
ATMs. Also, on page 8 he states that "It also seems unlikely a universal
biomolecular computer will be conceived." But he makes no attempt to
discuss the capabilities of the human mind, which is clearly a
biomolecular "computer" that transcends the capabilities of the Turing
machine. In addition, he also notes that "a radical revision in our view
of space and time might in the future necessity a radical revision of our
ideas about mechanical computability". I believe we should not wait for
such a revolution. Instead, we can state that we do not know what are the
limits of computation and encourage people to work on alternative models
of computation. To get stuck with the idea that the Turing machine is the
end of story is pure mysticism.
A.S.
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